• Transactions of the Korean Society of Mechanical Engineers A
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• 제30권4호
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• pp.393-401
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• 2006

The influences of stress triaxiality on ductile fracture have been investigated for various specimens and structures. With respect to a transferability issue, recently, the interests on local approaches reflecting micromechanical specifics are increased again due to rapid progress of computational environments. In this paper, the applicability of the local approaches has been examined through a series of finite element analyses incorporating modified GTN and Rousselier models as well as fracture toughness tests. The ductile crack growth of nuclear carbon steels is assessed to verify the transferability among compact tension (CT) specimens with different in-plane size. At first, the basic material constants were calibrated for standard CT specimens and used to predict fracture resistance (J-R) curves of larger CT specimens. Then, the in-plane size effects were examined by comparing the numerically estimated J-R curves with the experimentally determined ones. The assessment results showed that the in-plane size effect should be considered for realistic engineering application and the damage models might be used as useful tool for ductile fracture evaluation.

• Journal of the Korean Society for Precision Engineering
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• 제23권8호
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• pp.54-63
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• 2006

Enhancement methods of sensitivity to in-plane strain measurement by micro-ESPI(Electronic Speckle Pattern Interferometry) technique were proposed using TiN and Au thin films. Micro-tensile strain over the micro-tensile specimens, prepared in micro-scale by those films, was measured by micro-tensile loading system and micro-ESPI system developed in this study. The subsequent measurement of in-plane tensile strain in the micro-sized specimens was introduced using the micro-ESPI technique, and the micro-tensile stress-strain curves for these films were determined. To enhance the sensitivity to measurement of in-plane tensile strain, algorithms of the phase estimation by using curve fitting of inter-fringe and the discrete Fourier Transform with object-induced dynamic phase shifting were developed. Using these two algorithms, the micro-tensile strain-stress curves were generated. It is shown that the algorithms for enhancement of the sensitivity suggested in this study make the sensitivity to measurement of the in-plane tensile strain increase.

• Journal of the Korean Mathematical Society
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• 제53권2호
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• pp.461-473
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• 2016

Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$ and the equality holds if and only if C is a P loski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.

• Journal for History of Mathematics
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• 제29권5호
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• pp.295-314
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• 2016

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. We learned that dynamic programming in tropical algebraic geometry can be used to find the shortest path in graphs. We have also learned about the Bezout's Theorem, which is a theorem concerning the intersections of tropical plane curves, and the stable intersection principle.

• Bulletin of the Korean Mathematical Society
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• 제59권2호
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• pp.407-417
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• 2022

Archimedes proved that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and the chord AB is four thirds of the area of the triangle ∆ABP. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ℝ². As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.

• Journal of KIISE:Software and Applications
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• 제27권1호
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• pp.50-61
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• 2000

Recently the stereo vision based on conics has received much attention by many authors. Conics have many features such as their matrix expression, efficient correspondence checking, abundance of conical shapes in real world. Extensions to higher algebraic curves met with limited success. Although irreducible algebraic curves are rather rare in the real world, lines and conics are abundant whose products provide good examples of higher algebraic curves. We consider plane algebraic curves of an arbitrary degree $n{\geq}2$ with a fully calibrated stereo system. We present closed form solutions to both correspondence and reconstruction problems. Let $f_1,\;f_2,\;{\pi}$ be image curves and plane and $VC_P(g)$ the cone with generator (plane) curve g and vertex P. Then the relation $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ gives polynomial equations in the coefficient $d_1,\;d_2,\;d_3$ of the plane ${\pi}$. After some manipulations, we get an extremely simple polynomial equation in a single variable whose unique real positive root plays the key role. It is then followed by evaluating $O(n^2)$ polynomials of a single variable at the root. It is in contrast to the past works which usually involve a simultaneous system of multivariate polynomial equations. We checked our algorithm using synthetic as well as real world images.

• Structural Engineering and Mechanics
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• 제41권1호
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• pp.95-112
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• 2012

In order to analyze the experimental hysteretic behavior of the in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls (RGMACBMW), we have carried out the pseudo static testing on the six specimens of RGMACBMW. Based on the test results and shear failure characteristics, the shear force hysteretic curves and displacement envelope curves of the models were obtained and discussed. On the basis of the hysteretic curves a general skeleton curve of the shear force and displacement was formed. The restoring model was adopted to analyze the seismic behavior and earthquake response of RGMACBMW. The deformation capacity of the specimens was discussed, and the formulas for calculating the lateral stiffness of the walls at different loading stages were proposed as well. The average lateral displacement ductility factor of RGMACBMW calculated based on the test results was 3.16. This value illustrates that if the walls are appropriately designed, it can fully meet the seismic requirement of the structures. The quadri-linear restoring models of the walls degradation by the test results accurately reflect the hysteretic behaviors and skeleton curves of the masonry walls. The restoring model can be applied to the RGMACBMW structure in earthquake response analysis.

• Journal of the Korean Society for Precision Engineering
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• 제12권6호
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• pp.80-86
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• 1995

A method of eliminating the branch problem in driving crank center point plane for 3 position synthesis of 4 bar mechanism is introduced. By studying various transformation characteristics from the circle point plane into the center poi t plane, the curves in the center point plane transformed from the filemon line in circle point plane are analytically obtained, which will seperate the whole center point plane into many sub-areas for the selec- tion of the center point of the driving crank. And a simple method to identify which of the sub-areas will cause the branch problem is also presented. The method will allow the selection of the center point of driving crank without the branch problem.

• Honam Mathematical Journal
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• 제17권1호
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• pp.41-47
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• 1995

• Proceedings of the KWS Conference
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• 대한용접접합학회 2002년도 Proceedings of the International Welding/Joining Conference-Korea
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• pp.113-120
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• 2002

The effect of out-of-plane loads on the fatigue strength of welded steel structures is examined through fatigue tests with weldment of two fillet weld joint types. The results of the fatigue tests are compared with those under axial loads, on the basis of the hot spot stress range at the weld toe. From the result of the comparison, a method on how to incorporate the effect of the out-of-plane bending stress is proposed using design S-N curves derived from fatigue tests under the axial load. The proposed method is useful for rational assessment of the fatigue strength of fillet-welded structures, where combined stresses of the in-plane axial stress and the out-of-plane bending stress are induced simultaneously due to the complexity of applied loads and structural geometry.